US Secretary of State Condoleezza Rice has stressed the importance of Sunni Arabs being more involved in drafting Iraq's new constitution.

In a surprise visit to the country, Ms Rice said she and the Iraqi Prime Minister, Ibrahim al-Jaafari, had discussed mechanisms to achieve this.

She told American ABC television that Iraq's achievements in the past year had been remarkable.

But she said further political progress was vital to overcome the insurgency.

It's very hard what the Iraqis are being asked to do, which is cast off years and years of tyranny and dictatorship and come to political unity in what is a very complicated place

Condoleezza Rice

Ms Rice made the visit to hold talks with Iraq's new government on how to combat the mainly Sunni insurgency.

She insisted Iraq's security forces were making progress, but she arrived as the bodies of 34 people, some beheaded, were discovered dumped at several sites.

They included 13 men dumped in a shallow grave in Baghdad's impoverished Sadr City.

Eleven others were found in Iskandariya, just south of Baghdad.

More than 400 people have been killed in attacks by insurgents since Iraq's democratically elected government was announced at the end of April.

In other developments:

Sheik Qassim al-Gharawi, an aide to Iraq's top Shia cleric, Ayatollah Ali al-Sistani, is shot dead along with his nephew in Baghdad

Four people are killed and at least 15 injured when two suicide bombers attack the convoy of Raed Rashid, governor of Diyala province, in the town of Baquba, north-east of Baghdad; he escapes unharmed

Gunmen open fire on a senior industry ministry official as he travels through the Gazaliya district in Baghdad, killing him and his driver

Constitution concerns

Ms Rice said the insurgency could be beaten if Iraqis were offered a "strong political alternative".

There have been a string of attacks in recent weeks

But she said she was concerned that Sunni Muslims were not taking a full part in that process, and had only token representation on a committee set up to draft a new constitution.

Ms Rice added that the security forces in Iraq were "fighting a tough set of terrorists" and that the US military "will remain active in Iraq until Iraq can defend itself".

Addressing a news conference in Baghdad's heavily fortified Green Zone, with Mr Jaafari at her side, Ms Rice expressed support for the new Iraqi government, which was finally formed at the end of April - three months after the election.

"I have great confidence in the leadership that the Iraqi leaders have shown and in the dedication of the Iraqi people", she said.

"It's very hard what the Iraqis are being asked to do, which is cast off years and years of tyranny and dictatorship and come to political unity in what is a very complicated place."

Secrecy

Ms Rice is the first senior US figure to visit Iraq since the government was formed.

It is also her first visit to Iraq since being promoted to secretary of state earlier this year.

To ensure security, Mr Jaafari was only told of the plan on Friday.

Even the pilot flying Ms Rice's plane was not informed who his passenger was until she was safely on board, senior state department adviser Jim Wilkinson said.

Ms Rice's first stop was the city of Irbil in the Kurdish north, where she donned body armour to fly by helicopter for a meeting with Kurdish leader Massoud Barzani.